gssanova {gss} | R Documentation |
Fit smoothing spline ANOVA models to responses from selected
exponential families with cubic spline, linear spline, or thin-plate
spline marginals for numerical variables. Factors are also
accepted. The symbolic model specification via formula
follows the same rules as in lm
and glm
.
gssanova(formula, family, type="cubic", data=list(), weights, subset, offset, na.action=na.omit, partial=NULL, method=NULL, varht=1, prec=1e-7, maxiter=30, ext=.05, order=2)
formula |
Symbolic description of the model to be fit. |
family |
Description of the error distribution. Supported
are "binomial" , "poisson" , "Gamma" ,
"inverse.gaussian" , and "nbinomial" . |
type |
Type of numerical marginals to be used. Supported
are type="cubic" for cubic spline marginals,
type="linear" for linear spline marginals, and
type="tp" for thin-plate spline marginals. |
data |
Optional data frame containing the variables in the model. |
weights |
Optional vector of weights to be used in the fitting process. |
subset |
Optional vector specifying a subset of observations to be used in the fitting process. |
offset |
Optional offset term with known parameter 1. |
na.action |
Function which indicates what should happen when the data contain NAs. |
partial |
Optional extra fixed effect terms in partial spline models. |
method |
Score used to drive the performance-oriented
iteration. Supported are method="v" for GCV,
method="m" for GML, and method="u" for Mallow's CL. |
varht |
Dispersion parameter needed for method="u" .
Ignored when method="v" or method="m" are
specified. |
prec |
Precision requirement for the iterations. |
maxiter |
Maximum number of iterations allowed for performance-oriented iteration, and for inner-loop multiple smoothing parameter selection when applicable. |
ext |
For cubic spline and linear spline marginals, this option
specifies how far to extend the domain beyond the minimum and
the maximum as a percentage of the range. The default
ext=.05 specifies marginal domains of lengths 110 percent
of their respective ranges. Prediction outside of the domain
will result in an error. Ignored if type="tp" is
specified. |
order |
For thin-plate spline marginals, this option specifies
the order of the marginal penalties. Ignored if
type="cubic" or type="linear" are specified. |
The models are fitted by penalized likelihood method through the performance-oriented iteration, as described in the reference cited below.
Only one link is implemented for each family
. It is the
logit link for "binomial"
, and the log link for
"poisson"
, "Gamma"
, and "inverse.gaussian"
.
For "nbinomial"
, the working parameter is the logit of the
probability p; see NegBinomial
.
For family
"binomial"
, "poisson"
, and
"nbinomial"
, the score driving the performance-oriented
iteration defaults to method="u"
with varht=1
. For
family
"Gamma"
and "inverse.gaussian"
, the
default is method="v"
.
See ssanova
for details and notes concerning smoothing
spline ANOVA models.
gssanova
returns a list object of class
"gssanova"
which inherits from the class "ssanova"
.
The method summary
is used to obtain summaries of the
fits. The method predict
can be used to evaluate the
fits at arbitrary points, along with the standard errors to be used
in Bayesian confidence intervals, both on the scale of the link.
The methods residuals
and fitted.values
extract the respective traits from the fits.
For family="binomial"
, the response can be specified either
as two columns of counts or as a column of sample proportion plus a
column of weights, as in glm
.
For family="nbinomial"
, the response may be specified as two
columns with the second being the known sizes, or simply as a single
column with the common unknown size to be estimated through the
maximum likelihood method.
Chong Gu, chong@stat.purdue.edu
Gu, C. (1992), Cross-validating non Gaussian data. Journal of Computational and Graphical Statistics, 1, 169-179.
Methods predict.ssanova
,
summary.gssanova
, and fitted.gssanova
.
## Fit a cubic smoothing spline logistic regression model test <- function(x) {.3*(1e6*(x^11*(1-x)^6)+1e4*(x^3*(1-x)^10))-2} x <- (0:100)/100 p <- 1-1/(1+exp(test(x))) y <- rbinom(x,3,p) logit.fit <- gssanova(cbind(y,3-y)~x,family="binomial") ## The same fit logit.fit1 <- gssanova(y/3~x,"binomial",weights=rep(3,101)) ## Obtain estimates and standard errors on a grid est <- predict(logit.fit,data.frame(x=x),se=TRUE) ## Plot the fit and the Bayesian confidence intervals plot(x,y/3,ylab="p") lines(x,p,col=1) lines(x,1-1/(1+exp(est$fit)),col=2) lines(x,1-1/(1+exp(est$fit+1.96*est$se)),col=3) lines(x,1-1/(1+exp(est$fit-1.96*est$se)),col=3)